This Grade 9 Mathematics Algebra Notebook is an essential tool for any student studying math! It includes detailed notes and examples on key topics, to help students understand and master the subject. With its clear and concise format, it makes learning and mastering math concepts easier and more e...
, Key – core concepts
REAL NUMBERS NATURAL NUMBERS
NUMBERS “FAMILY”/SYSTEM
The number line consists of all the Rational
(Q) and Irrational (Q') numbers which
Even numbers : 2;4;6;8….
together form the set of Real (ℝ) numbers.
Odd numbers : 1;3;5;7…
UNREAL NUMBERS
Prime numbers : 2;3;5;7;11;13… (1 is not a prime
√−25 is an example of a non-real number. number)
There is no number that, when squared, will
Composite numbers : 4;6;8;9;10;12 (numbers with
equal -25.
more than 2 factors)
√−25 does not exist on the number line. Square numbers : 1;4;9;16;25…
The real and non-real numbers together
form the complex numbers. Cubic numbers : 1;8;27;64;125…
COUNTING NUMBERS
INTEGERS
RASIONAL NUMBER
any number that can be written as a fraction, i.e. a
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐴
or [where A & B ∈ Z ; B ≠ 0]
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐵
W All integers.
W All fractions.
W All terminating decimal fractions.
W All repeating decimal fractions.
IRRASIONAL NUMBERS
W All non-terminating, non-repeating decimal
Can only be written in a number form with infinite, numbers
non-repeating digits after the decimal point, the W Pi (π)
numbers can NOT be written as a FRACTION W √Positive non − square
3
W √Positive non − cubic
, Key – core concepts
BODMAS CALCULATIONS WITH BRACKETS ()
NB ! At minus - and brackets ()
Inside the bracket (-3)² = (-3)(-3) =+9
No bracket -3² =-(3)(3) = -9
Outside the bracket -(3)² =-(3)(3) = -9
CALCULATIONS WITH ROOTS √
+ or – under √ [first SIMPLIFY under the √]
W √16 + 9=√25
W √16 + 9≠√16 + √9
x or ÷ under the √ [divide √ and work out each
part's √ separately]
W √16 × 9=√144
SIGN RULES [X ÷] W √16 × 9=√16 × √9
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